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Games associated with products of eigenvalues of the Hessian

  • Received: 23 September 2022 Revised: 15 November 2022 Accepted: 16 November 2022 Published: 29 November 2022
  • We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length goes to zero, the value functions of the games converge uniformly to a viscosity solution of the partial differential equation. The classical Monge-Ampère equation is an important example under consideration.

    Citation: Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi. Games associated with products of eigenvalues of the Hessian[J]. Mathematics in Engineering, 2023, 5(3): 1-26. doi: 10.3934/mine.2023066

    Related Papers:

  • We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length goes to zero, the value functions of the games converge uniformly to a viscosity solution of the partial differential equation. The classical Monge-Ampère equation is an important example under consideration.



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